Exponential & Log Review

Exponential Functions

100

For the function y = 3^x, provide 3 points that you would use in a chart (x, y). One of the points must be negative.

What is (1, 3), (0, 1), (-1, 1/3)

200

The horizontal asymptote of y=(2^x) +9

is this.

What is y=9

300

What would the domain be for the following? f(x) = 5^x

What is (-inf, inf)

400

What would the range be for the following? f(x) = 5^x

What is (0, inf)

500

For exponential functions, the x-axis serves as a horizontal _______________.

What is asymptote

Logarithmic Functions

100

Convert to an exponent: log₈(1) = 0

What is 8⁰ = 1

200

Convert to logarithmic form e⁷ = 1096.63

What is ln(1096.63) = 7

300

Consider: y = log₂(x + 2). What is the x-intercept for this function?

What is -1

400

Consider: f(x) = log₂(x + 2). What is the domain of this function?

What is (-2, inf)

500

If y = 2^x and y = log₂(x)  then the two functions are _________________of each other.

What is inverses

Logarithmic Properties

100

Condense: log(3) + log(4)

What is log(12)

200

Evaluate: log(-1)

What is undefined

300

Use your calculator to evaluate: log₃(4)

What is 1.26

400

Rewrite as a single log: 7log₆(x) - log₆(3)

What is log₆(x⁷ / 3)

500

Expand log ((x³y²)/z)

What is 3log(x) + 2log(y) - log (z)

Common and Natural Logs

100

Evaluate: log(1000)

What is 3

200

Evaluate ln(e)

What is 1

300

Evaluate: ln(root e)

What is 1/2

400

Solve: log(x) = 2

What is 100

500

Solve: ln(x) = -3. Round to 4 decimal places.

What is .0498

Equations

100

solve 3^x=30 - Round to 3 digits after the decimal point. 

What is 3.096

200

solve 5^2x-3=10 - Round to 3 digits after the decimal point. 

What is 2.215

300

Solve log₃(3x) = 3

What is 9

400

solve ln(x) - ln(5) = 3 - Round to 2 digits after the decimal point.

What is 100.43

500

Solve 3e^3x-5 = 49 - Round to 3 digits after the decimal point

What is x = 2.598